Consider the 47.0 kg mountain climber in the figure below.

Question

(b) What is the minimum coefficient of friction between her shoes and the cliff?

Answer 1

I'm taking a guess at what's going on in this problem: You likely have a climber on some sort of slope, and you need to know basically how much friction they'll need to keep from slipping. Here are some things that can help:

1. The force of gravity can be broken down into components that are parallel and perpendicular to the slope. This helps us determine their motion along the slope.
2. F_parallel = mg*sin(Θ)
3. This is the component that is pulling the climber back down the slope.
4. F_{perpendicular} = mg*cos(Θ)
5. This is the component pulling her down in towards the mountain.
6. As long as there is no other support (like a rope pulling the climber up), this force will be equal and opposite to the normal force that the mountain is providing.
7. For a climber (with no other external forces) to keep from slipping, F_parallel must be equal and opposite to force of friction.
8. F_friction = μ* F_normal
9. Now you can plug in and solve
10. mg*sin(Θ) = μmgcos(Θ)
11. Note that the mass doesn't actually matter in this case.